Learning continuous models for continuous physics
[1];
[3];
- Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Google Research, Mountain View, CA (United States)
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); International Computer Sciences Institute (ICSI), Berkeley, CA (United States)
- Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); International Computer Sciences Institute (ICSI), Berkeley, CA (United States)
Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach is that ML models are typically trained on discrete data, using ML methodologies that are not aware of underlying continuity properties. This results in models that often do not capture any underlying continuous dynamics—either of the system of interest, or indeed of any related system. To address this challenge, we develop a convergence test based on numerical analysis theory. Our test verifies whether a model has learned a function that accurately approximates an underlying continuous dynamics. Models that fail this test fail to capture relevant dynamics, rendering them of limited utility for many scientific prediction tasks; while models that pass this test enable both better interpolation and better extrapolation in multiple ways. Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications.
- Research Organization:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- USDOE Laboratory Directed Research and Development (LDRD) Program; National Science Foundation (NSF)
- Grant/Contract Number:
- AC02-05CH11231; DMS-2319621
- OSTI ID:
- 2204781
- Alternate ID(s):
- OSTI ID: 2367186
- Journal Information:
- Communications Physics, Vol. 6, Issue 1; ISSN 2399-3650
- Publisher:
- Springer NatureCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Similar Records
Robust Carbon Dioxide Plume Imaging Using Joint Tomographic Inversion of Seismic Onset Time and Distributed Pressure and Temperature Measurements (Final Report)
COMPLEX NETWORKS IN CLIMATE SCIENCE: PROGRESS, OPPORTUNITIES AND CHALLENGES